[petsc-users] better way of setting dirichlet boundary conditions

[Bishesh Khanal]

On Tue, Aug 20, 2013 at 3:06 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Tue, Aug 20, 2013 at 7:19 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>
>> Hi all,
>> In solving problems such as laplacian/poisson equations with dirichlet
>> boundary conditions with finite difference methods, I set explicity the
>> required values to the diagonal of the boundary rows of the system matrix,
>> and the corresponding rhs vector.
>> i.e.  typically my matrix building loop would be like:
>>
>> e.g. in 2d problems, using DMDA:
>>
>> FOR (i=0 to xn-1, j = 0 to yn-1)
>>      set row.i = i, row. j = j
>>      IF (i = 0 or xn-1) or (j = 0 or yn-1)
>>             set diagonal value of matrix A to 1 in current row.
>>      ELSE
>>             normal interior points: set the values accordingly
>>      ENDIF
>> ENDFOR
>>
>> Is there another preferred method instead of doing this ? I saw functions
>> such as MatZeroRows()
>> when following the answer in the FAQ regarding this at:
>> http://www.mcs.anl.gov/petsc/documentation/faq.html#redistribute
>>
>> but I did not understand what it is trying to say in the last sentence of
>> the answer "An alternative approach is ... into the load"
>>
>
> Since those values are fixed, you do not really have to solve for them.
> You can eliminate them from your
> system entirely. Imagine you take the matrix you produce, plug in the
> values to X, act with the part of the
> matrix  that hits them A_ID X, and move that to the RHS, then eliminate
> the row for Dirichlet values.
>

Now I understand the concept, thanks! So how do I efficiently do this with
petsc functions when I am using DMDA which contains the boundary points
too? Conceptually the steps would be the following, I think, but which
petsc functions would enable me to do this efficiently, for example,
without explicitly creating the new matrix A1 in the following and instead
informing KSP about it ?
1) First create the big system matrix (from DM da) including the identity
rows for Dirichlet points and corresponding rhs, Lets say Ax = b.
2) Initialize x with zero, then set the desired Dirichlet values on
corresponding boundary points of x.
3) Create a new matrix, A1 with zeros everywhere except the row,col
positions corresponding to Dirchlet points where put -1.
4) Get b1 by multiplying A1 with x.
5) Update rhs with b = b + b1.
6) Now update A by removing its rows and columns that correspond to the
Dirichlet points, and remove corresponding rows of b and x.
7) Solve Ax=b



>    Matt
>
> Thanks,
>> Bishesh
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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